University of California at Berkeley

Physics 111 Laboratory

Basic Semiconductor Circuits Supplementary Material

Noise Generator

The Noise Generator should work on any W98, Win2K, or WinXP box equipped with a Soundblaster
compatible sound card.
To run the generator, first download
and extract the noise generator zip file "NoiseGenerator.zip" to a file,
and then run the file "Noise Generator.exe" [i.e. use the Run button
on the start menu and specify "Noise Generator.exe" (in the appropriate
directory.)]

You can use the generator to explore different types of noise.
Start by setting the program to "Gaussian White Noise" and "Generate Real
Time Data". Hit the "Generate" button, and the program will generate
a set of gaussian distributed data points, display their spectrum, and
play the resulting signal through the speakers. Take a look at the
amplitude histogram in the lower left corner; as expected, the noise is
gaussian. Generate several new data sets, and note how they all sound
alike. Then change the settings to "Generate Spectrum", and generate
a new data set. Here the program first generates a gaussian
distributed spectrum, and takes an inverse Fourier transform to find the
real time data, which it then plays over the speakers. Is the amplitude
histogram still gaussian? These two methods of generating noise are
formally identical. Also try "Uniform White Noise", which generates
uniform distributed noise instead of gaussian distributed noise.
These two types of noise are quite different mathematically, but sound
almost the same.

Change the settings to "1/f Noise", and generate some data sets.
Listen carefully: doesn't the noise sound like a distant ocean waves?
As you can see in the spectrum graph, the amplitude of the frequency components
in 1/f noise are inversely proportional to the frequency. 1/f noise
is very common in nature, and can be used to model phenomenon as disparate
as the curvature of a beach to the volume produced by a symphony orchestra
to the spectrum of noise from almost all semiconductor devices at low enough
frequencies. The prevalence of 1/f noise is one of the deep ques-tion
about our world, but nobody has a good explanation.

You might think that 1/f noise is just bandwidth limited white noise,
but it actually sounds quite different. Go back to the "Gaussian
White Noise" and "Generate Spectrum" settings, but this time set the low
pass frequency to 500, i.e. 500Hz, and listen to the sound. This
will produce white noise whose maximum frequency is 500Hz. It is
quite different than 1/f noise…more like the noise of a furnace.
Can you explain why?

Set the noise generator to "Shot Noise", and the "Average Number of
Shots per Sample" to 0.001. Shot noise is also called counting or
Poisson noise, and occurs whenever as an average number of samples is supposed
to arrive in a fixed time interval. An example is the number of electrons
per second that cross a fixed point in a wire carrying a "constant" current.
Despite the fact that the current is supposed to be constant, there will
be random fluctuations in the number of electrons. Another example
is the number of radioactive decays in ten seconds from a radioactive sample.
On the average, say, ten decays might be expected, but the number in any
given ten second interval will fluctuate. The size of the fluctuation
is proportional to the square root of the expected number of samples: if
you ex-pect an average of counts, the average fluc-tuation
will be . Note that the normalized number of fluctuations,
decreases as increases.

Now generate a shot noise data set. What does it sound like?
Change the "Average Number of Shots per Sample" to 1. Generate a
new data set. What does it sound like? Try setting the "Average
Number of Shots per Sample" to 100 and 10,000. See how the amplitude
histogram becomes gaussian? Is this consistent with the sound that
you hear? Note that the data set is normalized; can you explain why
the sound volume decreases at high "Average Number of Shots per Sample"?

Finally, change to "Line (60Hz) Noise". Generate some data sets,
and play with the "Harmonic Content" knob. Where have you heard this
sound before?